MinT - Best Known (69, 69+52, s)-Nets in Base 8

Best Known (69, 69+52, s)-Nets in Base 8

(69, 69+52, 354)-Net over F₈ — Constructive and digital

Digital (69, 121, 354)-net over F₈, using

3 times m-reduction [i] based on digital (69, 124, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 62, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(69, 69+52, 385)-Net over F₈ — Digital

Digital (69, 121, 385)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(69, 69+52, 24029)-Net in Base 8 — Upper bound on s

There is no (69, 121, 24030)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 18 799355 722271 800646 841239 172688 266307 139336 380771 650944 956333 998647 329078 280697 922273 151790 611471 557118 016670 > 8¹²¹ [i]